Mötley Crüe's 1989 album Dr. Feelgood impressed Metallica enough for the band to hire Bob Rock for The Black Album.
Metallica had heard Rock's production work on Dr. Feelgood and believed he could help them make a stronger, more focused record. The choice represented a significant change from the producers associated with several of Metallica's earlier albums.
Rock's methods challenged the band. He encouraged them to record as a unit, asked for more polished vocal performances, and pushed James Hetfield to strengthen the lyrics. The process produced frequent arguments but also helped create the album's broad, powerful sound.
Dr. Feelgood was Mötley Crüe's sixth studio album and became a major commercial success. Its connection to Metallica is specifically about Rock's production work, not a collaboration between the two bands.